Improved quantification of the rate of ocean warming

The increased concentrations of greenhouse gases in the atmosphere create an increase in Earth's thermal energy, which is mainly stored in the ocean. Quantification of the rate of increase in ocean heat content (OHC) is vital for understanding the current and future climate of Earth. Linear trend lines have been frequently used to quantify long-term rates of change, but are inappropriate because they cannot capture nonlinearity in trends, have large start- and end-point sensitivity, and the assumption of linearity is nonphysical. Here observed and model-based linear regressions with higher-order polynomial (quadratic), piecewise linear, and locally weighted scatterplot smoothing (LOWESS) are compared. Piecewise linear and LOWESS perform best in depicting multidecadal trends. It is shown that linear rates are valid for up to about 15-yr segments (i.e., it is valid to compute linear rates within a 15-yr time window). Using the recommended methods, ocean warming for the upper 2000 m increases from about 0 to 0.06 +/- 0.08 W m(-2) for 1958-73 to 0.58 +/- 0.08 W m(-2) for 2003-18, indicating an acceleration of ocean warming that happens in all four ocean basins and from near the sea surface to 2000 m. There is consistency between multimodel-mean historically forced climate models and observations, which implies that the contribution of internal variability is small for global 0-2000 m OHC. Notable increases of OHC in the upper ocean (i.e., 0-300 m) after about 1980 and the deeper ocean (300-2000 m) after the late 1980s are also evident. This study suggests alternative methods to those currently used to estimate ocean warming rates to provide a more accurate quantification of long-term Earth's energy changes.